Image scrambling based on Logistic uniform distribution

Abstract

Most algorithms of image scrambling transformation based on Logistic map are currently dedicated to permutation rules and methods without considering design philosophy. In this paper, we propose a new image bit permutation algorithm based on the Logistic map. This algorithm with firmly mathematic theory is designed by following the scientific course from theory to practice. According to the characteristics of chaotic sensitivity to initial condition and large key space, starting from Logistic map, the transformation which can generate uniformly distributed random variable in the interval based on Logistic at =4 is developed. Utilizing this generated uniform random variable, random permutation algorithm based on interchange position is obtained. For measuring permutation strength of the proposed random permutation algorithm, the corresponding permutation strength testing algorithm is designed. Based on this permutation algorithm, the image bit permutation algorithm is described. When used to image and compared with Baker Ye and Yoon algorithm, the proposed image bit permutation method exhibits large key space, extreme sensitivity to initial condition, effective capability for dissipating high correlation among pixels and increasing information about entropy value. Results show that this proposed scrambling scheme with firmly theoretical foundation can enhance image security significantly.